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Math Help - Volume as a function of x

  1. #1
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    Volume as a function of x

    I have a question in my assignment where i am not how to answer it.

    A rectangular box with volume 7 cubic metres has a square base with side length x metres. Express the surface area S of the box as a function of x.

    Surface area S = ?

    I also have these two questions that are along the same lines that i also don't know how to properly solve.

    2) The diameter of a spherical balloon is 12 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the balloon as a function of x.
    Note. The volume of a sphere with radius R is V=34 R^3

    Answer: The increase in volume is equal to ? cm^3

    and

    3) A rectangle has its base lying on the x− axis and its upper corners on the parabola y=41−x2. If the upper right corner is (st), express the area A of the rectangle as a function of s.

    The area A = ?

    Thank you in advance.
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  2. #2
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    The volume of a box with a square base will be

    V = x^2h.

    Since the volume is 7\,\textrm{m}^3 which means

    x^2h = 7

    h = \frac{7}{x^2}.


    The surface area is ....
    Last edited by mr fantastic; September 27th 2010 at 07:30 PM. Reason: PLease leave something for the OP to do.
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  3. #3
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    Quote Originally Posted by mmfoxall View Post
    I have a question in my assignment where i am not how to answer it.

    A rectangular box with volume 7 cubic metres has a square base with side length x metres. Express the surface area S of the box as a function of x.

    Surface area S = ?

    I also have these two questions that are along the same lines that i also don't know how to properly solve.

    2) The diameter of a spherical balloon is 12 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the balloon as a function of x.
    Note. The volume of a sphere with radius R is V=34 R^3

    Answer: The increase in volume is equal to ? cm^3

    and

    3) A rectangle has its base lying on the x− axis and its upper corners on the parabola y=41−x2. If the upper right corner is (st), express the area A of the rectangle as a function of s.

    The area A = ?

    Thank you in advance.
    1) Let the height of the box be h. Then 7 = x^2h => h = 7/x^2. Use the dimensions of the box to get S.

    2) Get the old volume, R = 6. Get the new volume, R = 6 + (x/2). Get the difference in volume. Note: The formula you posted for the volume of a sphere is wrong. Use Google to find the correct formula.

    3) Draw a picture. Width is 2s (why?). Height is h = t = 41 - s^2 (why?). A = ....
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